Solve for $x$ and $y$ using elimination. ${-3x+3y = -18}$ ${-4x-6y = -44}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ ${-6x+6y = -36}$ $-4x-6y = -44$ Add the top and bottom equations together. $-10x = -80$ $\dfrac{-10x}{{-10}} = \dfrac{-80}{{-10}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-3x+3y = -18}\thinspace$ to find $y$ ${-3}{(8)}{ + 3y = -18}$ $-24+3y = -18$ $-24{+24} + 3y = -18{+24}$ $3y = 6$ $\dfrac{3y}{{3}} = \dfrac{6}{{3}}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {-4x-6y = -44}\thinspace$ and get the same answer for $y$ : ${-4}{(8)}{ - 6y = -44}$ ${y = 2}$